Finding r for a Single Period Investment
You are considering a one year investment. If you put up $1,250, you will get back $1,350. What rate is this investment paying? First, in this single period case, the answer is fairly obvious. You are getting a total of $100 in addition to your $1,250. The implicit rate on this investment is thus $100/1,2508 percent. More formally, from the basic present value equation, the present value (the amount you must put up today) is $1,250. The future value (what the present value grows to) is $1,350. The time involved is one period, so we have:
$1,250=$1,350/(1+r )1
1+r =$1,350/1,250=1.08
r =8%
In this simple case, of course, there was no need to go through this calculation, but, as we describe next, it gets a little harder when there is more than one period.